Hey Mom!
My first baby, my daughter, weighed just over 5 pounds, full term. That was a bit of a blessing for me, because I was so small framed, the doctor didn't know if I'd be able to have her by myself naturally. But I did. I breast fed her and although she gained some weight, it wasn't much, so I tried to supplement with formula. She loved the formula and was done with nursing. I wasn't ready to quit, but as long as she was happy and eating, I got over it. She only weighed 12 pounds at a year old, so she was really tiny. The difference with my baby though, is that she ate everything. She loved food! She was eating everything we ate AND she was walking at 7 months. She was very bright and alert so there was no "failure to thrive" issue, by any means.
She's going to be 23 years old on October 30 so I couldn't possibly remember her percentiles off the top of my head, but she is still tiny. She is built just like my mom. She MAY be 5'2", but I think that depends on how spikey she has her hair on a given day. (My mom is barely 5 feet). I'm 5'8" and small framed, (my ring finger is size 4), her dad is 6'2" and very slim, but Angel is a little pixie just like my mother and very active and healthy.
I remember being so nervous about those percentiles, but luckily I had a great pediatrician who tested her to make sure she didn't have any maladies, which she didn't. The percentiles didn't apply to her. She was on her own little growth curve. But, like I said, he also wasn't concerned because she ate everything. There was nothing she didn't like. By 10 months old, she was eating mashed potatoes and gravy, baked chicken and fish, pasta, yams, green beams, brocolli, scrambled eggs. She hated baby food and wouldn't eat it and I realized it was just too bland for her. She wanted flavor so I started out by giving her some things from my plate and she loved it.
Keep introducing foods, get him his own little silverware if you haven't already and just give him some time to experiment with getting things on the spoon or picking it up and tasting it. Don't worry if he doesn't just eat it right away...let him get used to how it feels in his hands and on his tongue. He should get the hang of it. Kids will pick up dirt clods and stick them in their mouths, sooner or later a green bean will find it's way past his lips and he may well spit it out but not necessarily because he doesn't like it. It just feels strange compared to what he's used to. Just keep trying. Don't get stressed.
You said he started solids at 5 months, but it doesn't sound like he's eating them. And I know you don't want to give him formula, but he's going to be a year old in a couple of months so if he's not eating solids and he's not gaining weight by then, you're going to need to re-think that. I didn't like giving my baby formula either, but she liked it and I could easily keep track of exactly how much she was getting every day. It's what worked for her.
I wish you well, and hope you get some great advice.